1 Getting Started
1.7 The statistical forecasting perspective
Random futures
A forecast is an estimate of the probabilities of possible futures.
Random futures
A forecast is an estimate of the probabilities of possible futures.
Random futures
A forecast is an estimate of the probabilities of possible futures.
Random futures
A forecast is an estimate of the probabilities of possible futures.
Random futures
A forecast is an estimate of the probabilities of possible futures.
Random futures
A forecast is an estimate of the probabilities of possible futures.
Random futures
A forecast is an estimate of the probabilities of possible futures.
Random futures
A forecast is an estimate of the probabilities of possible futures.
Random futures
A forecast is an estimate of the probabilities of possible futures.
Random futures
A forecast is an estimate of the probabilities of possible futures.
“He who sees the past as surprise-free is bound to have a future full of surprises.” (Amos Tversky)
Statistical forecasting
- Thing to be forecast: a random variable, y_t.
- Forecast distribution: If {\cal I} is all observations, then y_{t} |{\cal I} means “the random variable y_{t} given what we know in {\cal I}.
- The “point forecast” is the mean (or median) of y_{t} |{\cal I}
- The “forecast variance” is \text{var}[y_{t} |{\cal I}]
- A prediction interval or “interval forecast” is a range of values of y_t with high probability.
- With time series, {y}_{t|t-1} = y_t | \{y_1,y_2,\dots,y_{t-1}\}.
- \hat{y}_{T+h|T} =\text{E}[y_{T+h} | y_1,\dots,y_T] (an h-step forecast taking account of all observations up to time T).
